NEW YORK -- Twenty-four hours before the series finale, the Yankees were at a crossroads of sorts -- so close to the 52nd playoff berth in franchise history, yet frustrated by three straight losses to the Red Sox. Missed opportunities had plagued them, and the anticipation in a frustrated clubhouse was building.

But on Thursday night, in the 10,000th win in the franchise's storied history -- a 4-1 victory over the Red Sox at rainy Yankee Stadium -- the Yankees finally turned the corner, clinching an American League Wild Card spot. The Yanks could clinch home-field advantage for the AL Wild Card Game presented by Budweiser with one more win or one Astros loss.

"I think it's extremely gratifying. With what we went through this year, where people figured that we would be at the end of the year, what these guys did, these guys to me did a lot on heart and hard work," Girardi said. "We have a lot of injuries, we have age on this team; we dealt with a lot of stuff, but they always kept fighting and they always seemed to bounce back. When things started to look bad, they would bounce back. They did it again tonight."

Girardi on clinching a berth

BOS@NYY: Girardi discusses reaching the postseason

10/1/15: Yankees manager Joe Girardi discusses clinching a postseason berth and how his team will prepare for the Wild Card game

Beltran led off the second with a homer, and later in the inning, Brendan Ryan hit an RBI single to left field to score John Ryan Murphy, who had walked. That put the Yankees ahead, 2-0. The Red Sox answered with a run in the fifth when Mookie Betts delivered a base hit to score Deven Marrero. Bird went deep in the seventh and Refsnyder hit one out in the eighth to make it 4-1.

Beltran's solo homer

BOS@NYY: Beltran crushes a solo shot the opposite way

10/1/15: Carlos Beltran puts the Yankees on the board in the 2nd with an opposite-field solo home run

"You're in the dance, anything can happen. I think any team that gets in is capable of winning a championship," Alex Rodriguez said. "The one thing about baseball is you play for eight months and there is no lucky breaks. You've got to prove that you've got be a postseason team. So, the fact that we have a good brotherhood, that we play together as a team, I like our chances."

Beltran on CC, playoffs

BOS@NYY: Beltran discusses clinch, CC's gutsy start

10/1/15: Carlos Beltran discusses the gritty start by CC Sabathia and meeting the Yankees' season-long goal of reaching the postseason

MOMENTS THAT MATTEREDLiving by the home run: Beltran and Bird have been forces to be reckoned with, and that trend continued. Beltran concluded the final homestand with four runs, two doubles, two homers, six RBIs and two walks. His solo shot in the second inning was his 19th homer, and he's recorded at least 15 homers 14 times Bird, who hit eight homers in September, now has 11. That's the most by a Yankee in his first Major League season after debuting in August or later. Refsnyder's shot was his second of the year.

Bird's solo blast

BOS@NYY: Bird launches a solo shot into the bullpen

10/1/15: Greg Bird hammers Jean Machi's offering into the Yankees bullpen, giving New York a 3-1 lead in the 7th inning

"It's unbelievable," Bird said. "I mean, just being a part of this team and getting to come up here and help these guys out, I followed them throughout the year, obviously. They put in a lot of hard work so just being able to come up and contribute is huge. I've said it a thousand times, I just had to get ready for it and prepare for it and be ready if they needed me. It's just a special feeling just for this group and being a part of the 10,000 wins, it's hard to explain it. It's hard."

Betts blast knocked down by wind:After drilling two homers to beat the Yankees on Wednesday, it looked like Betts had come through again with a runner on. But his drive to deep left in the seventh was knocked down by a chilly wind as left fielder Chris Young made the catch in front of the wall, preserving a 2-1 lead for the Yankees.

Betts' flyout to the track

BOS@NYY: Wind knocks down Betts' deep fly ball

10/1/15: Mookie Betts' deep fly ball carries to the track in left, but the wind knocks it down and Chris Young reels in the catch

"Mookie hits that ball and we thought it was a home run. The wind knocked it down and it was something that was out of our control. Mookie did his job right there," said Red Sox interim manager Torey Lovullo. "It was unfortunate because the game changes in that situation and we execute on the mound a little differently. It happened and my congratulations to the Yankees."

Warren back in the bullpen:Adam Warren became a starter again Sept. 15 after Nathan Eovaldi went down with right elbow inflammation, but Thursday, Girardi used Warren out of the bullpen to help lock up one of the most important games of the year. Warren excited the Yankee Stadium crowd in the sixth when he made a beautiful behind-the-back stop on Sandy Leon's grounder to end the inning. The play elicited a huge smile from Warren, who pitched three scoreless innings of one-hit ball.

Warren tosses three scoreless

BOS@NYY: Warren shuts down Red Sox over three innings

10/1/15: Adam Warren enters the ballgame in the 6th and strikes out three over three scoreless frames to keep the Red Sox offense at bay

"I'm not saying that he won't be a starter if you move on, but we knew that on Tuesday, if we were to get in, he would be in the bullpen and we wanted to prepare for that and just to have a bridge to that," Girardi said. "Every good club that I've been on has seemed to have a guy like Adam Warren that is able to do so many different things for you as a pitcher. I first saw it in Ramiro Mendoza where he would spot start and do those things."

Hill strong again for Sox: Hill didn't get a shutout or strike out 10, but he was solid for his fourth straight start since returning to the the Majors. Over six innings, the lefty gave up four hits and two runs, walking three and striking out six. Hill (1.55 ERA) didn't allow more than three runs in any of his four starts, and he could be a candidate to sign with the Red Sox as a free agent this offseason.

Hill holds Yanks to two runs

BOS@NYY: Hill fans six, holds Yankees to two runs

10/1/15: Rich Hill goes six innings, holding the Yankees to two runs on four hits and three walks while striking out six batters

"They went well," said Hill. "I threw the ball the way I knew I could throw it. That's all I can say, really. I think if you look at the overall body of work, there was a lot to build off of from there. I'm looking forward to next year." More >

QUOTABLE
"It feels great. I came up here in 2008 and my first year, we missed the playoffs. After that we were in it four years in a row; you take it for granted. It feels good feeling the champagne burning your eyes. I saw a couple guys with the goggles on earlier and I made them take it off because it's a good feeling. It's a big accomplishment. We're excited about this opportunity." -- Brett Gardner

"Oh man, is that an understatement. With all the stuff I went through in 2014, I talk about how dark those days were. To come back this year and be part of such a special team, such a special group of guys ... we truly are a family and we've built a great brotherhood in here." -- Rodriguez, on if he appreciates this playoff berth

SOUND SMART WITH YOUR FRIENDS
Betts extended his on-base streak to 34 games, the longest active streak in the AL. Over his past 11 games, Betts is hitting .413 with 12 runs, six doubles, three homers and six RBIs.

Betts' RBI single

BOS@NYY: Betts cuts the deficit with an RBI single

10/1/15: Mookie Betts plates Deven Marrero with a single to center, pulling the Red Sox to within one run in the 5th

WHAT'S NEXTRed Sox:Rookie lefty Henry Owens (3-4, 3.84 ERA) will make his final start in the opener of a three-game series in Cleveland. The first pitch is scheduled for 7:10 p.m. ET. Owens is coming off a fine performance against the Orioles, when he fired 7 2/3 shutout innings in a win.

Yankees:The Yankees will head to Baltimore for a three-game set to close the regular season, with rookie righty Luis Severino set to face the O's for the first time. Against the O's, the Yankees are 9-7 and 2-4 at Camden Yards.

Ian Browne is a reporter for MLB.com. Read his blog, Brownie Points, follow him on Twitter @IanMBrowne and listen to his podcast. Grace Raynor is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.